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Fitting canine cancer incidences through a conventional regression model assumes constant statistical relationships across the study area in estimating the model coefficients. However, it is often more realistic to consider that these relationships may vary over space. Such a condition, known as spatial non-stationarity, implies that the model coefficients need to be estimated locally. In these kinds of local models, the geographic scale, or spatial extent, employed for coefficient estimation may also have a pervasive influence. This is because important variations in the local model coefficients across geographic scales may impact the understanding of local relationships. In this study, we fitted canine cancer incidences across Swiss municipal units through multiple regional models. We computed diagnostic summaries across the different regional models, and contrasted them with the diagnostics of the conventional regression model, using value-by-alpha maps and scalograms. The results of this comparative assessment enabled us to identify variations in the goodness-of-fit and coefficient estimates. We detected spatially non-stationary relationships, in particular, for the variables related to biological risk factors. These variations in the model coefficients were more important at small geographic scales, making a case for the need to model canine cancer incidences locally in contrast to more conventional global approaches. However, we contend that prior to undertaking local modeling efforts, a deeper understanding of the effects of geographic scale is needed to better characterize and identify local model relationships.

Approximately 1.5 million people, mostly children, die annually due to disease attributed to diarrhea reflecting urgent needs for improved understanding of associations between the disease and potential risk factors. Numerous epidemiological studies found spatially varying (non-stationary) disease associations attributable to changing geographic or demographic context. Spatial non-stationarity implies that average relationships from statistical models fitted to the whole study area might be inappropriate since they do not reflect local conditions. Spatial modeling techniques such as geographically weighted regression (GWR) have limitations in providing statistically robust analysis of spatial non-stationarity. Thus, there is a need for development or expansion of modeling techniques to address this issue. Using data for pediatric diarrheal mortality in Brazil in 2000, and different risk factors, we develop an analytical framework to determine regions of similar (stationary) local associations by combining GWR and max-p regionalization. We fit statistical models to these regions, and compare goodness-of-fit and regionally varying coefficients to the national-scale model measures. The proposed framework allows us to examine (a) impact of non-stationarity for regions of different geographic extent with acceptable statistical power, (b) the explanatory power of each risk factor in each region, and (c) if these regions reflect changing data quality or truly existing variations in putative associations., (Copyright © 2012 Elsevier Ltd. All rights reserved.)